Muon acceleration in non-scaling FFAG rings is surveyed. Such rings are essentially alternating-gradient rings with focusing strong enough to achieve a dispersion that is small enough to hold muons within a momentum range of a factor of two to three in a single aperture. The longitudinal dynamics of acceleration outside buckets is presented first. The scaling laws relating the lattice and RF system parameters are discussed. Several lattices that have been proposed for such FFAG rings are shown. The tunes cover many integers, and acceleration implies crossing many integral and half-integral resonances. The leading terms in path length and travel time are linear and quadratic in the momentum error. The apertures are calculated. The parameters of the rings are compared. Acceleration is demonstrated. An electron model of such an FFAG ring is presented, which would allow one to experimentally study the novel aspects of non-scaling FFAG rings.


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